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Perpendicular Distance of a Point from a Line

If the line y...

Question

If the line $y = m x + a$ meets the parabola $y^{2} = 4 a x$ in two points whose abcissa are $x_{1}$ and $x_{2}$ , then $x_{1} + x_{2} = 0$ if

m = - 1

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m = 1

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m = 2

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m = \frac{- 1}{2}

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Solution

The correct option is C $m = 2$
$y^{2} = 4 a x$

$y = m x + a$ On substituting $y$ from this line to the parabola equation

$(m x + a)^{2} = 4 a x$
$\Rightarrow m^{2} x^{2} + (2 a m - 4 a) x + a^{2} = 0$

Sum of roots $= x_{1} + x_{2} = \frac{- (2 a m - 4 a)}{m^{2}} = 0$

So, $m = 2$

Suggest Corrections

Similar questions

If the line $y = m x + a$ meets the parabola $y^{2} = 4 a x$ at two points whose abscissas are $x_{1}$ and $x_{2},$ then $x_{1} + x_{2} = 0$ if

y = m x + a

y^{2} = 4 a x

x_{1}

x_{2},

m

x_{1} + x_{2} = 0

y = m x + a

y^{2} = 4 a x

x_{1}

x_{2},

m

x_{1} + x_{2} = 0

y = m x + a

y^{2} = 4 a x

x_{1}

x_{2}

x_{1} + x_{2} = 0

y^{2} = 4 a x

(x_{1}, y_{1})

(x_{2}, y_{2})

x_{1}, x_{2} + y_{1} y_{2} =

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